Nontrivial zeros of the Riemann zeta function on the celestial circle

TL;DR

This paper links the nontrivial zeros of the Riemann zeta function to the scaling dimensions of conformal operators in a holographic celestial conformal field theory, offering a novel geometric perspective.

Contribution

It reformulates the Riemann zeta function within a holographic framework, connecting its zeros to conformal operator dimensions on the celestial circle.

Findings

Zeros of the zeta function relate to conformal operator scaling dimensions.

Holographic reformulation provides new insights into number theory.

Potential implications for the spectrum of celestial conformal field theory.

Abstract

In this short letter, we reformulate the Riemann zeta function using the holographic framework of the celestial conformal field theory. For spacetime dimension larger than our Minkowski spacetime $M^4$, the Riemann zeta function is connected with the sum of the conformal primary wavefunctions evaluated over a chain of points on the holographic boundary. Using analytic continuation, it follows that the nontrivial zeros of the Riemann zeta function is connected with the scaling dimension of conformal operators on the celestial circle. We discuss possible considerations with the spectrum of the celestial conformal field theory, number theory and topology.